Radiation from loops next to a sphere in a radome

Radiation from multiple circular loop antennas of different radii and of different current values is considered. Parallel circular loops lie on an imaginary spherical surface of radius a. A conducting or dielectric sphere of radius ba and of outer radius d could be placed around the loops. The circular loops are parallel to the xy-plane and their centers are on the z-axis. The centers of the sphere and the dielectric shell are both at the origin. Eigenfunction series solutions are assumed in different regions of the problem. The unknown coefficients are computed by enforcing boundary conditions at the interfaces of these different regions.